Question

Which of the following shows that polynomials are closed under subtraction when two polynomials, (5x2 3x 4) − (2x2 5x − 1), are subtracted? 3x2 − 2x 5; will be a polynomial 3x2 − 2x 5; may or may not be a polynomial 3x2 8x 3; will be a polynomial 3x2 8x 3; may or may not be a polynomial.

Answer 1

The closure property under subtraction is shown when the correct

result from the subtraction of polynomials is also a polynomial.

Response:

• The option that shows that polynomials are closed under subtraction is; 3·x² - 2·x + 5 will be a polynomial.

How is the option that shows the closure property found?

The closure property under subtraction for the polynomials is condition

in which the result of the difference between two polynomials is also a

polynomial.

The given polynomials being subtracted is presented as follows;

(5·x² + 3·x + 4) - (2·x² + 5·x - 1)

Which gives;

(5·x² + 3·x + 4) - (2·x² + 5·x - 1) = 3·x² - 2·x + 5

Given that the result of the subtraction, 3·x² - 2·x + 5, is also a

polynomial, we have, that the option that shows that polynomials are

closed under subtraction is; 3·x² - 2·x + 5 will (always) be a polynomial.

Learn more about closure property here:

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